SR22 instructor pilot reported an near midair collision with another aircraft not on CTAF.

Attributes
ACN	1679418
Time
Date	201908
Local Time Of Day	1201-1800
Environment
Flight Conditions	VMC
Light	Daylight
Aircraft 1
Make Model Name	SR22
Operating Under FAR Part	Part 91
Flight Phase	Cruise
Flight Plan	None
Aircraft 2
Make Model Name	Skyhawk 172/Cutlass 172
Operating Under FAR Part	Part 91
Person 1
Function	Pilot Not Flying
Qualification	Flight Crew Commercial Flight Crew Flight Instructor Flight Crew Instrument Flight Crew Multiengine
Experience	Flight Crew Last 90 Days 100 Flight Crew Total 1100 Flight Crew Type 550
Events
Anomaly	Conflict NMAC Deviation - Procedural Clearance Deviation - Procedural Published Material / Policy
Miss Distance	Horizontal 450 Vertical 0

Narrative:

While completing a training flight with a student over the hudson river; about a mile south of the verrazano bridge; we nearly collided with the pilot(s) of a cessna 172 who were not communicating on the CTAF. A third party yelled at us on the CTAF to advise us that a cessna was straight ahead at the same altitude; opposite direction. Seconds later I saw the aircraft and took control from my student; executing an evasive right turn. I'm estimating that we were just over 400 ft. Laterally from the other aircraft; at the same altitude.

Original NASA ASRS Text

Title: SR22 Instructor Pilot reported an NMAC with another aircraft not on CTAF.

Narrative: While completing a training flight with a student over the Hudson River; about a mile south of the Verrazano Bridge; we nearly collided with the pilot(s) of a Cessna 172 who were not communicating on the CTAF. A third party yelled at us on the CTAF to advise us that a Cessna was straight ahead at the same altitude; opposite direction. Seconds later I saw the aircraft and took control from my student; executing an evasive right turn. I'm estimating that we were just over 400 ft. laterally from the other aircraft; at the same altitude.

Data retrieved from NASA's ASRS site and automatically converted to unabbreviated mixed upper/lowercase text. This report is for informational purposes with no guarantee of accuracy. See NASA's ASRS site for official report.